Interval type-2 fuzzy neural networks version of the Stone-Weierstrass theorem

The main purpose of this study is to state conditions that guarantee an interval type-2 triangular fuzzy (IT2TF) neural network can approximate continuous IT2TF functions. To make a more efficient calculation with IT2TF numbers, the sum and the product of two IT2TF numbers are constructed. These concepts are used in the definition of IT2TF polynomials. Moreover, the present study provides a mathematical framework to show that IT2TF polynomials are a compact Hausdroff space. Based on this concept we establish an interval type-2 fuzzy neural networks version of the Stone-Weierstrass theorem which enables approximation by a special class of IT2TF neural networks on the set of all monotonic and continuous IT2TF functions. Finally, a numerical example is given to illustrate the results.